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Three-Loop Beta Function in QED for SU(3) and Dimensional Transmutation in QCD

This paper presents the calculation of the three-loop beta function for quantum electrodynamics (QED) in the fundamental representation of SU(3), detailing the conditions for fixed points and dimensional transmutation. It demonstrates that the two-loop beta function exhibits a zero, highlighting implications for infrared fixed points in quantum chromodynamics (QCD). The study includes an exploration of Banks-Zaks fields interacting with the Standard Model, providing explicit examples within supersymmetric QCD and discussing operator dimensions and Feynman rules.

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Three-Loop Beta Function in QED for SU(3) and Dimensional Transmutation in QCD

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  1. Unparticle PhysicsMike Berger September 6, 2007

  2. Beta function QED 3-loop beta function for SU(3) fundamental representation = 11 – (2/3)NF = 1/2 = 102 – (38/3)NF b0=0 b1=0 = 33/2 =16.5 = 153/19 = 8.05 2-loop beta function has a zero (fixed point) if Results can be generalized to group G with rep R

  3. IR UV

  4. QCD (without quark masses) is a classically scale invariant theory Dimensional transmutation = 11 – (2/3)NF LQCD

  5. Banks-Zaks fields with infrared fixed point interact with SM fields Dimensional transmutation of BZ fields The operator dimension dU can be non-integral Explicit example in SQCD with strongly coupled fixed point: 3/2 NC < NF < 3 NC for SU(NC) gauge group

  6. Feynman rules (scalar)

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